Q. 1 F5.0( 2 Votes )
Without actually performing the long division, state whether the following rational numbers have terminating or non-terminating repeating (recurring) decimal expansion.
Given rational number is
is terminating if
a) p and q are co-prime &
b) q is of the form of 2n 5m where n and m are non-negative integers.
Firstly, we check co-prime
7 = 7 × 1
80 = 2 × 2 × 2 × 2 × 5
7 and 80 have no common factors
Therefore, 7 and 80 are co-prime.
Now, we have to check that q is in the form of 2n5m
80 = 24 × 5
So, denominator is of the form 2n5m where n = 4 and m = 1
Thus, is a terminating decimal.
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